Terminal Velocity of Spherical Particles

FIG. 6-61 Terminal velocities of spherical particles of different densities settling in air and water at 70°F under the action of gravity. To convert fhs to m/s, multiply by 0.3048. (From Lapple, etal.. Fluid and Particle Mechanics, University of Delaware, Newark, 1951, p. 292. )... 

This approach, however, necessitates the knowledge of the terminal velocity of spherical particles under wide ranges of conditions which is currently... 

By definition, the terminal velocity of a particle (ut) is the superficial gas velocity which suspends an isolated particle without translational motion—i.e., the terminal free fall velocity for that particle. From force balance on the particle, the terminal velocity for an approximately spherical particle can be shown to be... 

A. Haider and O. Levenspiel, Drag coefficient and terminal velocity of spherical and nonspherical particles, Powder Technol., 1989, 58, 63-70. 

Since they tend to flatten out, they offer more resistance to falling and have lower terminal velocities than spherical particles. This effect is not important for freely falling particles having diameters less than a few hundred micrometers. Table 5.3 gives terminal settling velocity data for raindrops of various diameters. Above about 6 mm in diameter the drops fracture and break up while falling. 

Calculate the terminal settling velocities of spherical particles of sizes 50, 100 and 1000 pm respectively. Solid density is 2.8x10 kg/m, liquid density is 1.0x10 kg/m and liquid viscosity is l.Ox 10 N s/m. ... 

Machac, 1., Siska, B. and Machacova, L., Terminal falling velocity of spherical particles moving through a Carreau model fluid , Chem. Eng. Proc., accepted for publication in early 2000... 

The above equations are valid for spherical isometric particles with negligible wall effeet. If the terminal velocity of a particle is available, the above equations can be used to estimate the minimum fluidization veloeity as well. 

The region of particle Reynolds number between 10 and 0.5 is known as the Stokes or streamline flow region. When a particle settles by gravity, it reaches a constant settling velocity, known as the terminal velocity. In terms of a force balance, the gravity force on the particle is equal to the sum of the drag force plus the buoyancy force. The terminal velocity for spherical particles in the Stokes region can be easily derived. The velocity is equal to ... 

Now consider a stationary particle held in position by a stream flowing upward at just the terminal velocity of the particle, as shown in Figure 2-8. The fluid far away from the particle is in laminar flow, but in the wake of the particle, eddies form. A two dimensional slice of the flow provides a picture that is similar, in our intuitive context, to the surface currents behind a rock in a flowing stream. The eddies are relatively stationary in space and are easy to observe. They are typically round (or elliptical) in cross-section and maintain their size, which invites our intuition to jump to the idea of a coherent spherical (or ellipsoidal) eddy. We need to examine a general turbulent flow more carefully before making that assumption. 

Fig. 4. Terminal velocities in air of spherical particles of different densities settling at 21°C under the action of gravity. Numbers on curves represent tme (not bulk or apparent) specific gravity of particles relative to water at 4°C. Stokes-Cunningham correction factor is included for settling of fine particles.

Alternatively, the model of Shiller and Naumann is commonly used for the prediction of terminal velocity of a spherical particle ... 

Many particles are not spherical and so will not have the same drag properties as spherical particles. The effective diameter for such particles is often characterized by the equivalent Stokes diameter, which is the diameter of the sphere that has the same terminal velocity as the particle. This can be determined from a direct measurement of the settling rate of the... 

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